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3 years ago

Use distance formula d=√(X2 – X1 )2 + (X2 – X1 )2, calculate the distance r from the origin to the point r (-2, √5).

1 answer:

7 0

$d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} \\d = \sqrt{(\sqrt{5} - (-2))^{2} + (\sqrt{5} - (-2))^{2}} \\d = \sqrt{(\sqrt{5} + 2)^{2} + (\sqrt{5} + 2)^{2}} \\d = \sqrt{(4 + 4\sqrt{5} + 5) + (4v + 4\sqrt{5} + 5)} \\d = \sqrt{0 + 0} \\d = \sqrt{0} \\d = 0$

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What is the answer to 9x + 10 = -8

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Answer: the answer should be x=-2

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Write the equation of the parabola in vertex form.<br> vertex (2,4), point (3,-2)<br> f(x)=

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3 years ago

A collection of 30 gems, all of which are identical in appearance, are supposedto be genuine diamonds, but actually contain 8 wo

levacccp [35]

Answer:

Step-by-step explanation:

From the given information:

There are 30 collections of gems, of which 8 are worthless;

Thus, the number of the genuine diamonds = 30 - 8 = 22.

Let X = random variable;

X consider the value as 0 (for 2 worthless stone selection),

X = 1200(1 worthless stone & 1 genuine stone)

X = 2400 (2 genuine stones selected)

However, the numbers of ways of selecting and chosen Gems can be estimated as:

$(^n_r) = (^{30}_2) \\ \\ \implies \dfrac{30!}{2!(30-2)!} \\ \\ \implies \dfrac{30!}{2!(28)!} \\ \\ \implies \dfrac{30*29*28!}{2!(28)!} \\ \\ \implies \dfrac{30*29}{2*1} \\ \\ \implies 435$

Thus;

$Pr (X = 0) = \dfrac{(^8_2)}{435}$

$Pr (X = 0) = \dfrac{\dfrac{8!}{2!(8-2)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8!}{2!(6)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8*7*6!}{2!(6)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8*7}{2*1}}{435} \\ \\ Pr (X = 0) = 0.0644$

$P(X =1200) = \dfrac{(^{8}_{1})(^{22}_{1})}{435}$

$P(X =1200) = \dfrac{ \dfrac{8!}{1!(8-1)!}) ( \dfrac{22!}{1!(22-1)!}) }{435}$

$P(X =1200) = \dfrac{ (8) ( 22) }{435}$

$P(X =1200) =0.4046$

$Pr (X = 2400) = \dfrac{(^{22}_2)}{435}$

$Pr (X = 2400) = \dfrac{\dfrac{22!}{2!(22-2)!}}{435} \\ \\ Pr (X = 2400) = \dfrac{\dfrac{22!}{2!(20)!}}{435} \\ \\ Pr (X = 2400) = \dfrac{\dfrac{22*21*20!}{2!(20)!}}{435} \\ \\ Pr (X =2400) = \dfrac{\dfrac{22*21}{2*1}}{435} \\ \\ Pr (X = 2400) = 0.5310$

To find E(X):

E(X) = (0 × 0.0644) + (1200 × 0.4046) + (2400 × 0.5310)

E(X) = 0 + 485.52 + 1274.4

E(X) = 1759.92

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3 years ago

The points in the table lie on a line. Find the slope of the line

NikAS [45]

Answer:

Step-by-step explanation:

(y2-y1)/(x2-x1)=m

(10-2)/(3-1)

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2 years ago

The boys kept adding sand, and ten minutes later the volume of the sand cone had increased by 30%. What is the exact volume of t

RideAnS [48]

Answer:

a) 84π b) 109.2π

Step-by-step explanation:

The formula to find this is v=πr^2h/3

r=d/2. so the radius (r) is 6 because you have to divide the diameter (12) by 2. and the height is 7. so, 6^2=36 and 36x7=252.

252/3=84

and because the question is asking for the EXACT value, you need to just put the pi symbol next to it. Final answer for a is 84π

B) you need to find 30% of 84, which is 25.2 and add it to 84, and you will get 109.2! Final answer is 109.2π.

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3 years ago